Here's one possibility I've been using.
It doesn't quite hit max range with psycho (don't use if you want max range), but it does have a little extra health, and resists from even tougher.
The only issue is to be fully optimised, allowing two eye shots from max AP, you either need Jet, or a +ap sniper and a +ap set of CA.
To increase hit chance, it also can use +agility CA and then take Buffout.
It's certainly shitty to need so much statted crap to fully optimise a build, but it still works moderately well without it. Uses a .223 pistol fine
Note: Bloody Mess is optional if you don't want to die at 0 hp, so is loner. Basically pick whatever traits you want, there aren't really any that benefit snipers anyway.